To find [tex]\( g(f(2)) \)[/tex], we need to follow these steps:
1. Evaluate [tex]\( f(2) \)[/tex]:
- Start with the function [tex]\( f(x) = x^2 + 2x \)[/tex].
- Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 2^2 + 2 \cdot 2
\][/tex]
- Compute the exponentiation and multiplication:
[tex]\[
f(2) = 4 + 4 = 8
\][/tex]
- Therefore, [tex]\( f(2) = 8 \)[/tex].
2. Evaluate [tex]\( g(f(2)) \)[/tex]:
- Now that we know [tex]\( f(2) = 8 \)[/tex], we use this value in the function [tex]\( g(x) \)[/tex].
- The function [tex]\( g(x) = 3x - 4 \)[/tex].
- Substitute [tex]\( x = 8 \)[/tex] into the function:
[tex]\[
g(8) = 3 \cdot 8 - 4
\][/tex]
- Compute the multiplication and subtraction:
[tex]\[
g(8) = 24 - 4 = 20
\][/tex]
- Therefore, [tex]\( g(8) = 20 \)[/tex].
So the final answer to the question [tex]\( g(f(2)) \)[/tex] is [tex]\( 20 \)[/tex].
Hence, the correct choice is:
[tex]\( \boxed{20} \)[/tex]
